Source: 30:05 juncture. Prof. Steven Cassedy. The following is based on YouTube's transcript that lacks formatting, and whose errors I corrected. Sorry for the strange numbering; I originally deleted the time junctures, but then decided to keep them after a few sentences.
How do we prove that there are such things that relies on the principle of sympathetic vibration? If an object is vibrating at a certain frequency, a nearby object object tuned to that same frequency will begin to vibrate together sympathetically with the first object. So let's say I want to prove that this low C on the piano (this one down here) has the next two overtones: that's the C above it and the G above that as part of its overtone series. What I do is: I hold
down the next C up without playing it
that releases the damper so that the
string can vibrate, and then I play the
lower C as hard as I can and release it
to release its damper.
If you're still hearing that upper C,
it's on the overtone series; it means
that the lower C had that and made
it sympathetically vibrate similarly
with the G above it. And on a great big
piano like this you can kind of hear it
resonate. In fact, it resonates for some
reason, that I don't know, more than the
C which is closer to it and similarly
for frequencies farther out on the
series, but it would be very very
difficult to hear that on an instrument
like this even in a hall with the
acoustics like the ones in Prebys Hall.
All right. So we don't hear these overtones
separately when we hear a C played on
the piano, but they're certainly there.
I ask about the bolded. Please answer simply; I am ignorant in physics or acoustics.